In 1975, Pippenger and Golumbic [1]} proposed the inducibility problem: determine the maximum possible density of induced copies of a \(k\) -vertex graph \(H\)  that can be contained in an \(n\) -vertex graph. Here, we take the density to be the number of copies of \(H\)  divided by \(\binom{n}{k}\) , the number of \(k\) -vertex induced subgraphs of the host graph. For a \(k\) -vertex graph \(H\)  and \(n\) -vertex graph \(G\) , we denote by \(I(H,G)\)  the number of induced copies of \(H\)  in \(G\) , and by \(i(H,G) := I(H,G)/\binom{n}{k}\)  the density of \(H\)  in \(G\) . If \(G\)  is an \(n\) -vertex graph which maximizes \(I(H,G)\)  over all \(n\) -vertex graphs, then we say that \(G\)  is extremal and introduce the notations \(I(H,n) = I(H,G)\)  and \(i(H,n) = i(H,G)\) . Finally, we define the inducibility of \(H\)  as \(\displaystyle \lim _{n\rightarrow \infty } \frac{I(H,n)}{\binom{n}{k}} = \lim _{n\rightarrow \infty } i(H,n)\) .
